In the study of the regularity of solutions of porous medium type equations it is often assumed that solutions can be constructed as weak limits of sufficiently smooth solutions to a regularized problem, see for example [1]}, [2]}, or it is assumed that the solution is a classical solution, see [3]}.
This is done to justify some of the computations and it is always stressed that the obtained modulus of continuity solely relies on the data and is independent of the approximation.
This assumption is not considered to be restrictive in view of typical existence proofs and is therefore often omitted, for instance, see [4]}, [5]}.
